Line tangent to the curve

  1. 1. The problem statement, all variables and given/known data

    For what values of a and b is the line 3x+y=b tangent to the curve y=ax^3 when x=5 ?

    3. The attempt at a solution
    I believe i would need to find the equation of the tangent to y=ax^3 when x=5 then that should be equal to -3x+b=y if im not mistaken but im not sure what to do from here to solve for a and b.

    Any leads in the right direction or insight if this is the entirely wrong approach would be greatly appreciated!
  2. jcsd
  3. HallsofIvy

    HallsofIvy 41,255
    Staff Emeritus
    Science Advisor

    Well, yes, that's just a restatement of the problem! You know that the slope of y= -3x+ b is -3. What connection is there between the slope of a tangent line and the function itself?
  4. thank you for the quick reply hallsofivy. I had -0.04 instead of -3/75 giving me the wrong answer for the online homework webpage which was confusing me. After using -3/75 instead it counts it as correct :(
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